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Statistical mechanics of voting

David A. Meyer·Thad A. Brown
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Abstract

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of cohesion/diversity among agents in terms of random matrix models---ensembles of statistical mechanics models---and compute quantitative answers in some representative cases.

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BibTeXRIS

David A. Meyer, Thad A. Brown. 1998-06-29. Statistical mechanics of voting. https://doi.org/10.1103/physrevlett.81.1718

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